Like with normal civ, your first priority should be setting up a basic territory, while increasing commerce. As monkeyfinger said, education is pretty important here. Look at your starting location and the immediate surroundings before making a final decision though. If you start with 3 or 4 sources of reachable dye or silk, consider going calender. Same with gold/gems and mining. Hook up your starting res. rather sooner than later.
With one or two exceptions, always get an economy going before specialising down a specific tech lane.
About these tech lanes: where civ4 is pretty steamlined, requiring you to research all available techs sooner or later, FFH is a lot more specialised. You pretty much have to pick a specific area to focus on, like melee units, magic, mounted units (hippus!), recon, archery or devine troops. Different paths appeal to different civs. This is more clearly described in the manual, but looking at a civ's UU's and UB's can give a clear indication as well.
Generally, civs like the bannor and the grigori are recommended for first-time players.
The bannor because their playstyle is pretty lineair. Focus on melee troops (metal working line)early game (axemen), and founding the religion "Order", while cottage-spamming like crazy (seriously, as much as you can possibly cope with). Then head for their unique civic "crusade". Start a war with someone, watch units pop up from each developed town, and go on a general rampage. Don't forget these units disappear when you're not at war though, so declare on the next target before you finish off the first
.
The grigori have 2 features which are unique to FFH, but these two make them a nice learner civ.
The first is their leader trait "agnostic". This basically means, they can't adopt a religion, they can't even research the techs for those religions. This means they've got one HUGE choice they don't have to make anymore, making the game a bit simpler.
The other feature are their "adventurers". These are combat units, generated like GP's (don't worry, you'll pop your fist before you're even capable of getting other types of GP's). They can be upgraded to every normal combat unit, with 1 added promotion: "hero". This promo allows them to slowly gather exp over time (1 point per turn up to 100 exp), as well as opening up some specific very useful promotions (heroic strenght and defence, and twincast).
With the grigori, you can more easily adapt to the less units, higher experience fights that FFH offers compared to normal BTS, without worrying about religions too much.